rrcd: Program for Constructing Resolvable Row-column Designs

  1. Introduction
  2. Using rrcd
  3. Output
  4. Examples
  5. References

Introduction

A resolvable row-column design (RCD) is an arrangement of r kxs arrays each of which is a complete replicate of v=ks treatments. We say this resolvable RCD is of size (r,k,s). Chapter 6 of John & Williams (1995) gives an excellent summary of resolvable RCDs. In this note this book is abbreviated as JW.

rrcd is a Gendex module for constructing optimal or near-optimal resolvable RCDs. The approach used by rrcd is to permute the treatments within the blocks of a resolvable incomplete block design (IBD) used as the column component of the RCD. This IBD can be constructed by either the IBD module or the ALPHA module of the Gendex toolkit. The optimality criterion and the algorithm implemented in rrcd are discussed in Nguyen & Williams (1993). In this note this paper is abbreviated as NW.

Using rrcd

Let's assume all Gendex class files are in the directory c:\gendex and suppose you want to construct a resolvable RCD of size (r,k,s)=(2,3,3). The following is the file alpha.txt in the working directory which contains a resolvable IBD of size (v,k,r)=(9,3,2) with blocks as columns (Note: the replicates of a resolvable IBD should be separated by blank lines):

4     8     6
7     2     0
1     5     3

6     3     8
1     7     0
5     2     4

At the working directory, issue the following command at the Command Prompt (case is important and no space is allowed before/after the equal sign):

java -cp c:\gendex rrcd in=alpha.txt

rrcd will start running and after try 1, the plan of the constructed design for this try will be displayed at the terminal window (as the ratio E/U reaches 1) and rrcd stops:

rrcd 10.0: Program for Constructing Resolvable Row-Column Designs
(c) 2018 Design Computing (http://designcomputing.net/)

Note: Best resolvable RCD for v=9, r=2, k=3 and s=3

Try	iter	f	E(col)	E(row)	E	E/U	Concurrences
1	1	36	0.667	0.667	0.5	1.0	1(36) 

Plan (as k x s matrices) for try 1 using seed 1533519934058:

4	2	6	
7	5	0	
1	8	3	

6	7	8	
1	2	0	
5	3	4	

Note: rrcd used 0.138 seconds.
Note: rrcd.htm has been created.

Note that the default random seed is the one obtained from the system clock and the default number of tries is 1000. You can change these default values by specifying the seed number and the number of tries, e.g.

java -cp c:\gendex rrcd=alpha.txt seed=1234 tries=1000

Output

The result of the best try is displayed in the terminal window and is also saved in the file rrcd.htm in the working directory. This file can be read by a browser such as IE or Google Chrome. Information for this try includes:

  1. Try number;
  2. The number of iterations;
  3. The objective function f.
  4. The row, column and row-column efficiency E of the constructed design and the ratio E/U where U is the upper bound of a resolvable RCD of size (r,k,s). The program automatically stops if this ratio reaches 1.
  5. The distribution of the concurrences of this design;
  6. The design plan and the associated random seed;
  7. The time in seconds rrcd used to construct the above design.

Examples

  1. A resolvable RCD of size (r,k,s)=(5,4,4) (http://designcomputing.net/gendex/rrcd/r1.html).
  2. A resolvable RCD of size (r,k,s)=(3,4,4) (http://designcomputing.net/gendex/rrcd/r2.html).
  3. A resolvable RCD of size (r,k,s)=(4,3,4) (http://designcomputing.net/gendex/rrcd/r3.html).
  4. A resolvable RCD of size (r,k,s)=(4,9,5) (http://designcomputing.net/gendex/rrcd/r4.html).
  5. A resolvable RCD of size (r,k,s)=(4,4,5) (http://designcomputing.net/gendex/rrcd/r5.html).
  6. A resolvable RCD of size (r,k,s)=(2,6,7) (http://designcomputing.net/gendex/rrcd/r6.html).
  7. A resolvable RCD of size (r,k,s)=(2,4,7) (http://designcomputing.net/gendex/rrcd/r7.html).
  8. A resolvable RCD of size (r,k,s)=(2,5,10) (http://designcomputing.net/gendex/rrcd/r8.html).

Notes:

References

John, J.A. & Williams E.R. (1987) Cyclic designs and computer-generated designs. New York: Chapman & Hall.
Nguyen, N-K & Williams, E.R. (1993) An algorithm for constructing optimal resolvable row-column designs. Austral. J. Statist. 35, 363-370.

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